The prominent energy management technique, Dynamic Voltage and Frequency Scaling (DVFS), was recently shown to have direct and adverse effects on system reliability. In this work, we investigate static and dynamic reliability-aware energy management schemes for a set of periodic real-time tasks to minimize energy consumption while preserving system reliability. Focusing on EDF scheduling, we first show that the static problem is NP-hard and propose two task-level utilizationbased heuristics. Then, we develop a job-level dynamic (on-line) scheme by building on the idea of wrappertasks, to monitor and manage dynamic slack efficiently in reliability-aware settings. Our schemes incorporate recovery tasks/jobs into the schedule as needed for reliability preservation, while still using the remaining slack for energy savings. Simulation results show that all the proposed schemes can achieve significant energy savings while preserving the system reliability. Moreover, the energy savings of the static heuristics are close to those of the static optimal solution by a margin of 5%.